A certain medication comes in the form of a capsule, as
shown below. The fluid inside the capsule contains
several ingredients, including the active medication.
4 mm
nearest tenth.
V= mm3
If the density of the active medication in the liquid is
0.7 mg/mm3. how many milligrams of the active
medication are in one capsule? Round to the nearest
tenth.
mg
5.6 mm

Answer:

(3b + c)(a - 2b)

Step-by-step explanation:

Given

3ab - 6b² - 2bc + ac ← Rearranging

= 3ab + ac - 6b² - 2bc (factor the first/second and third/fourth terms )

= a(3b + c) - 2b(3b + c) ← factor out (3b + c) from each term

= (3b + c)(a - 2b)

Answer:

(a-2b)(3b-c)

Step-by-step explanation:

3ab-6b^2-2bc+ac

Let's rearrange

3ab+ac-6b^2-2bc

Let's factorise

a(3b+c)-2b(3b+c)

(a-2b)(3b+c)

Since the answer cannot be solved further

The answer is (a-2b)(3b+c)

Answer:

A. True

Step-by-step explanation:

I could be wrong

True, The number of seconds in any hour has an order of magnitude of 3.

The order of magnitude is the power of 10, a number is raised to when it's in scientific notation.

Given,

No. of seconds in an hour = 3600 seconds

In scientific notation

No. of seconds in an hour = 3.6 × 10³ seconds

Here, 10 is being raised to the third power.

Hence, The number of seconds in any hour has order of magnitude of 3.

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Answer:

The answer is qualitative as the prices to be won are different.

Hope this helps

Answer:

8/5

Step-by-step explanation:

To find the slope given two points

m = (y2-y1)/(x2-x1)

    = (4- -4)/(1 - -4)

   = (4+4)/(1+4)

   =8/5

Answer: answer is 8/5

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

Since a board is cut into four parts and we are to determine the fraction for each piece

So it will be 1/total number of pieces

Which will be 1/4

So the fraction for each board will be 1/4

Given:

The given triangle is a right triangle.

The length of the hypotenuse is 31 units.

The length of the leg is 23 units.

One of the angle is x.

We need to determine the value of x.

Value of x:

The value of x can be determined using the trigonometric ratio.

Thus, we have;

[tex]sin \ \theta=\frac{opp}{hyp}[/tex]

Substituting [tex]\theta=x[/tex], the side opposite to the angle x measures 23 units and the hypotenuse is 31.

Thus, we have;

[tex]sin \ x=\frac{23}{31}[/tex]

Dividing, we get;

[tex]sin \ x=0.74[/tex]

Taking [tex]sin ^{-1}[/tex] on both sides of the equation, we get;

[tex]x=sin^{-1}(0.74)[/tex]

[tex]x=47.7[/tex]

Rounding off to the nearest whole integer, we get;

[tex]x=48[/tex]

Thus, the value of x is 48°

Hence, Option c is the correct answer.

Answer:

c

Step-by-step explanation:

your slope will always be infront of x

Answer:

  $107,000

Step-by-step explanation:

Austin's salary in his 19th year will include his base pay and 18 raises:

  $80,000 + 18×$1500 = $107,000

Austin's salary in his 19th year would be $107,000.

Answer:

f(x) = 3x² - 24x + 53

Step-by-step explanation:

Given

f(x) = 3(x - 4)² + 5 ← expand the factor using FOIL

     = 3(x² - 8x + 16) + 5 ← distribute by 3 and simplify

     = 3x² - 24x + 48 + 5

     = 3x² - 24x + 53 ← in standard form

Answer:

D

Step-by-step explanation:

When reflecting points across the x axis, and x coordinate remains the same and y-coordinates become the opposite of the original.

Answer:

it is D

Step-by-step explanation:

Joanna deposited $132000 and her interest amount is $359730.35

Step-by-step explanation:

Monthly deposit = $275

Interest = 5.6%

Time = 40 years

After 40 years her account balance = $491730.35

If she deposit $275 monthly then after 40 years she will have deposited ,

= 275 x 12 x 40

= $132000

The remaining is her interest amount.

Interest amount = 491730.35 - 132000

= $359730.35

Joanna deposited $132000 and her interest amount is $359730.35

Work Shown:

7 ways to pick the president.

6 ways to pick the VP

5 ways to pick the secretary

7*6*5 = 210 ways to pick the three people from a pool of seven. Order matters because the positions are different. Note the count down from 7 to 6 to 5 which indicates that any given person cannot run for more than one office.

You can use the permutation formula with n = 7 and r = 3

The permutation formula is [tex]_n P_r = \frac{n!}{(n-r)!}[/tex] where the exclamation marks represent factorials.

There are 210 distinct ways to assign seven candidates to three different class offices (president, vice president, and secretary), based on permutation principles.

The question involves finding out in how many ways three different class offices (president, vice president, and secretary) can be filled from a pool of seven candidates. This is a permutations problem because the order in which the candidates are chosen matters (as the offices are distinct). To solve this, we use the permutation formula. For the first office, you have 7 choices (any of the 7 candidates can fill it). Once the first position is filled, you are left with 6 candidates for the second office. Similarly, after filling the second office, there are 5 candidates left for the third office.

Therefore, the total number of ways to fill these positions is the product of these choices, which is calculated as:

7 × 6 × 5 = 210 ways.

This means there are 210 distinct ways to assign these seven candidates to the three available class offices, assuming no candidate can hold more than one office simultaneously.

Answer:

is it 57

Step-by-step explanation:

Answer:

x = 57

Step-by-step explanation:

x and 57° are vertical angles and congruent, thus

x = 57

Answer:

− 8x+9

Step-by-step explanation:

Answer:

Wayne has 10.05 gallons left.

Step-by-step explanation:

16 3/4 times 2/5 is 6.7

16 3/4 minus 6.7 is 10.05

Wayne has 327/20 gallons of fuel left in his car.

Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator.The number on the bottom of the line is called the denominator.

Now it is given that,

Amount of fuel in the car = 16 3/4 gallons = 67/4 gallons

Amount of fuel used = 2/5 gallons

Therefore,

Amount of fuel left in the car = Amount of fuel in the car - Amount of fuel used

⇒ Amount of fuel left in the car = 67/4 - 2/5

⇒ Amount of fuel left in the car = 327/20 gallons

Thus, Wayne has 327/20 gallons of fuel left in his car.

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t + 5 + 3t = 1

Group like terms:

t+3t+5= 1

Add similar elements:

4t+5=1

Subtract 5 from both sides:

4t+5-5 = 1-5

Simplify:

4t= -4

Divide both sides by 4:

4t/4 = -4/4

Simplify:

t= -1

Your Answer Is t= -1

plz mark me as brainliest :)

Answer:

h = 6

Step-by-step explanation:

Since 1/2 times the base length times the height equals the area, just work your way backwards to get the answer!

It looks like this

(1/2)8 * h = 24

First multiply 1/2 by 8 to get 4

then divide 4 out of both sides so that h = 6!

Thank me later :)

Answer:

6 is the answer

Step-by-step explanation:

The answer is The scale factor of the enlargement is 3.2. Square the scale factor to get 10.24. Find the area of the original figure, which is 32. Multiply 32 and 10.24 to get the area of the enlarged figure, which is 327.68.                                    I took the asinmate

The area of the enlarged figure is 327.68 units²

What is scaling ?

It is the method to resize drawing with comparing to true size of object which uses proportion or ratio. For example, Mapping of earth, drawing prototype of automobiles.

It is given that :

A small rectangle has a length of 8 and width of 4 and a large rectangle has a length of 25.6 and width of a, then

The area of the small rectangle is :

 area = length · width

 area = (8)(4) = 32 units²

The scale factor is ...

 scale factor = greater length / smaller length

                      = 25.6/8

                      = 3.2

The area of the greater rectangle will be equals to the small rectangle area multiplied by the square of the scale factor:

(32 units²)(3.2²) = 327.68 units²

Therefore, the area of the enlarged figure is 327.68 units²

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Answer:

what do you need help with?

Step-by-step explanation:

Answer: yes i will be your tutor what is your question.

Step-by-step explanation:

That is true, you multiply the length by the width in a rectangle, and you do the same in a square.

Answer:

The range is -16.3

Step-by-step explanation:

The range is the highest number minus the lowest number and if we take a look at this data -5, 0.7, -1.9, 3.5, -9.2, 7.1, -0.6 ,-8.7 ,2.2 ,0.6, we can see that the lowest value is -9.2 and the highest value is 7.1, so we have to minus the lower value from the higher value

-9.2 - 7.1 = -16.3

The range is -16.3

Answer:

3.99

Step-by-step explanation:

I = PRT

I = 6.65 x .10 x 6

I = 3.99

Answer:

3.99

Step-by-step explanation:

Answer:

see attached

Step-by-step explanation:

Each cube root or square root lies:

∛800: Between 2 and 3

∛101: Between 4 and 5

∛90: Between 4 and 5

∛20: Between 2 and 3

√7: Between 2 and 3

√20: Between 4 and 5

√90: Between 9 and 10

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Here are the steps to find whether each cube root or square root lies between 2 and 3, 4 and 5, or 9 and 10:

Start with the first cube root or square root, ∛800.

Estimate the value of the root.

For ∛800, we can estimate that it's between 8 and 9, since 8 cubed is 512 and 9 cubed is 729.

So, ∛800 must be somewhere in between.

Determine which range the estimated value falls into.

Since 8 is between 2 and 3, ∛800 must also be between 2 and 3.

Repeat the process for the remaining cube roots and square roots, using the same ranges.

Here are the results:

∛800: Between 2 and 3

∛101: Between 4 and 5

∛90: Between 4 and 5

∛20: Between 2 and 3

√7: Between 2 and 3

√20: Between 4 and 5

√90: Between 9 and 10

Thus,

Four of the roots lie between 2 and 3, two lies between 4 and 5, and one lies between 9 and 10.

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Answer:

The fraction increase by ( [tex]0.047=4.7\:\%[/tex] ) if its numerator is

increased by 25% and its denominator is increased by 20%.

Step-by-step explanation:

As

[tex]100\%\mathrm{\:in\:fractions}=\:1[/tex]

[tex]25\%\mathrm{\:in\:fractions}=\:\frac{1}{4}[/tex]

[tex]20\%\mathrm{\:in\:fractions}=\frac{1}{5}[/tex]

so

Increase in 25% means

[tex]100\%\:+25\%\:=\frac{5}{4}[/tex]    

Increase in 20% means

[tex]100\%\:+20\%\:=\frac{6}{5}[/tex]

Thus the fraction becomes

[tex]\:\frac{\frac{5}{4}\times \:n}{\frac{6}{5}\times \:d}[/tex]                  

[tex]=\frac{\frac{5}{4}n}{\frac{6d}{5}}[/tex]

[tex]\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\times \:d}{b\times \:c}[/tex]

[tex]=\frac{5n\times \:5}{4\times \:6d}[/tex]

[tex]=\frac{25n}{24d}[/tex]

[tex]=1.0417\left(\frac{n}{d}\right)[/tex]

[tex]=1\left(\frac{n}{d}\right)+0.047\left(\frac{n}{d}\right)[/tex]

As

[tex]0.047=4.7\:\%[/tex]

Therefore, the fraction increase by ( [tex]0.047=4.7\:\%[/tex] ) if its numerator is

increased by 25% and its denominator is increased by 20%.

Answer:

The y intercept is 6 and the slope is -3.

Please see the attached graph.

Answer:

35 Meters

Step-by-step explanation:

Ratio is 12

What I mean by that is 2 turns into 24 because you multiply 12 to it. Same thing for 420, except for the fact that you divide it (working backwards). So 420 divided by 12 equals 35:)  Enjoy your day

Answer:

the answer is 35 meters.

Answer:

c) 10

Step-by-step explanation:

You do 5 C 3 ( because you are choosing 3 from the remaining 5).

5C3 = 5!/(3!2!) = 10

Answer:

C 10

Step-by-step explanation:

He has 6 colours to choose 3 from.

One of them is green, so he just needs to choose 2 from the remaining 5.

That's,

5C2 = 10

Answer:

The correct option is;

c. Because the p-value of 0.1609 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of juice in all the bottles filled that day does not differ from the target value of 275 milliliters.

Step-by-step explanation:

Here we have the values

μ = 275 mL

275.4

276.8

273.9

275

275.8

275.9

276.1

Sum = 1928.9

Mean (Average), = 275.5571429

Standard deviation, s = 0.921696159

We put the null hypothesis as H₀: μ₁ = μ₂

Therefore, the alternative becomes Hₐ: μ₁ ≠ μ₂

The t-test formula is as follows;

[tex]t=\frac{\bar{x}-\mu }{\frac{s}{\sqrt{n}}}[/tex]

Plugging in the values, we have,

Test statistic = 1.599292

[tex]t_{\alpha /2}[/tex] at 7 - 1 degrees of freedom and α = 0.05 = ±2.446912

Our p-value from the the test statistic = 0.1608723≈ 0.1609

Therefore since the p-value = 0.1609 > α = 0.05, we fail to reject our null hypothesis, hence the evidence suggests that the mean does not differ from 275 mL.

Answer:

Because the p-value of 0.1609 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of juice in all the bottles filled that day does not differ from the target value of 275 milliliters.

Step-by-step explanation:

I took the quiz and got it right

Answer:

Logan has the greater probability of winning

Step-by-step explanation:

Colton=1/20

=0.05

So the probability of Colton is 0.05

Logan=15%

=15/100

=0.15

So the probability of Logan is 0.15

When comparing the two,it was observed that the Logan has greater probability of winning